USES OF POTENTIOMETER

Uses of potentiometer –

• Measurement of emf of cell-

 

 

 

 

Let ,

E is the  emf of  driver cell  and ,  E₁  is the emf of cell to be measured

Here potential gradient K= [ {E / (R+r)} r]/l .

Let l₁  is the length of the wire from zero end where galvanometer shows no deflection

Then E₁ = K l₁

E₁ =   [ {E / (R+r)} r]/l X l₁

• Comparison of EMFs of two cells

 

 

• 

  To find the emf of two cells we connect the two cells with the potentiometer  as shown in figure  having emfs E₁  and E₂  .

  When 1 and 2 is connected together let null point is at length l₁  from zero end,

  Then E₁ = K l₁ …….(i)

  Again when 2 and 3 are connected , null point  is at length  l₂ from zero end ,

  Then  E₂ = Kl₂ ……..(ii)

  By dividing (i) and (ii) we get E₁ /E₂ = l₁ / l₂ ………..(req. equation)

  To find the internal resistance of a cell –

  

 

Let,

E – is the emf of the cell of which we have to find the internal resistance

R – is the external resistance connected with  the cell

R –  internal resistance of the cell

Let initially  switch K’ is off and l₁ is the length of the null point from the zero end .

then E = K l₁ ……….(i)

After that switch K’ is switched on then the null point is at l₂  from zero end

then ( potential across R )       V = K l_{2 ………} (ii)

E/V = l₁ /l₂ …………..(iii)

But,  internal resistance r = [(E/V)-1] x R ……………..(iv)

So, from equation (iii) and (iv)

r =  [(l₁ / l₂ )-1] x R …….(req. equation)